On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds

Details On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds

2010-09-22

arxiv.org/abs/1009.4419v1

Mathematics

Algebraic Geometry

22 pages, to appear in Transactions of the AMS

Scientific paper

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $K$-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersections threefolds.

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